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Radiative instability of the flow around a rotating cylinder in a stratified fluid

Published online by Cambridge University Press:  07 February 2011

XAVIER RIEDINGER ,
STÉPHANE LE DIZÈS  and
PATRICE MEUNIER
XAVIER RIEDINGER
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre, CNRS/Universités Aix-Marseille I and II, 49, rue F. Joliot-Curie, BP 146, F-13384 Marseille CEDEX 13, France
STÉPHANE LE DIZÈS*
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre, CNRS/Universités Aix-Marseille I and II, 49, rue F. Joliot-Curie, BP 146, F-13384 Marseille CEDEX 13, France
PATRICE MEUNIER
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre, CNRS/Universités Aix-Marseille I and II, 49, rue F. Joliot-Curie, BP 146, F-13384 Marseille CEDEX 13, France
*
†Email address for correspondence: [email protected]
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Abstract

The stability of the flow around a rotating cylinder in a fluid linearly stratified along the cylinder axis is studied numerically and experimentally for moderate Reynolds numbers. The flow is assumed potential and axisymmetric with an angular velocity profile Ω = 1/r2, where r is the radial coordinate. Neglecting density diffusion and non-Boussinesq effects, the properties of the linear normal modes are first provided. A comprehensive stability diagram is then obtained for Froude numbers between 0 and 3 and Reynolds numbers below 1000. The main result is that the potential flow, which is stable for a homogeneous fluid, becomes unstable for Froude number close to one and for Reynolds numbers larger than 360. The numerical results are then compared with experimental results obtained using shadowgraph and synthetic Schlieren techniques. Two symmetrical helical modes are found to be simultaneously unstable. We show that these modes exhibit an internal gravity wave structure extending far from the cylinder in agreement with the theory. Their wavelength and frequency are shown to be in good agreement with the numerical predictions for a large range of Froude and Reynolds numbers. These experimental results are the first indisputable evidence of the radiative instability.

JFM classification

Geophysical and Geological Flows: Stratified flows Vortex Flows: Vortex instability Geophysical and Geological Flows: Waves in rotating fluids
Type
Papers
Information
Journal of Fluid Mechanics , Volume 672 , 10 April 2011 , pp. 130 - 146
Copyright
Copyright © Cambridge University Press 2011

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References

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Riedinger et al. supplementary movie

Synthetic schlieren visualisation. Vertical density gradient pattern associated with the radiative instability for Re=343 and F=1.01. Speed x2. The size of the image is $40*27$ cm$^2$.

Download Riedinger et al. supplementary movie(Video)
Video 7.9 MB

Riedinger et al. supplementary movie

Synthetic schlieren visualisation. Vertical density gradient pattern associated with the radiative instability for Re=343 and F=1.01. Speed x2. The size of the image is $40*27$ cm$^2$.

Download Riedinger et al. supplementary movie(Video)
Video 8.1 MB